This paper proposes a common and tractable framework for analyzing
different definitions of fixed and random effects in a contant-slope
variable-intercept model. It is shown that, regardless of whether
effects (i) are treated as parameters or as an error term, (ii) are
estimated in different stages of a hierarchical model, or whether (iii)
correlation between effects and regressors is allowed, when the same
information on effects is introduced into all estimation methods, the
resulting slope estimator is also the same across methods. If different
methods produce different results, it is ultimately because different
information is being used for each methods.